Question : $\triangle \mathrm{RMS}$ is right-angled at M. The length of the base, RM = 4 cm and the length of perpendicular MS = 3 cm. Find the value of $\sec R$.
Option 1: $\frac{3}{4}$
Option 2: $\frac{5}{4}$
Option 3: $\frac{4}{5}$
Option 4: $\frac{2}{5}$
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Correct Answer: $\frac{5}{4}$
Solution :
$\triangle \mathrm{RMS}$ is a right-angled triangle
⇒ $SR^2=SM^2+MR^2$
⇒ $SR^2=3^2+4^2=9+16=25$
⇒ $SR=\sqrt{25}=5$
$\therefore$ $\sec R =\frac{SR}{MR}=\frac{5}{4}$
Hence, the correct answer is $\frac{5}{4}$.
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